Yes, there are several ancient Greek New Testaments available. They are listed under the “GREEK (GRC) – Κοινη” entry in the list of available Bibles here: http://www.biblegateway.com/versions/. Currently there are four ancient Greek New Testaments available:
- SBL Greek New Testament
- 1550 Stephanus New Testament
- 1881 Westcott-Hort New Testament
- 1894 Scrivener New Testament
You can search or look up passages in the Greek texts like you would with any other Bible.